Tehran has blamed Saudi "mismanagement" for the stampede, which took place after two waves of pilgrims converged on a narrow street, causing hundreds to suffocate or be trampled.

"If it were proved that some [authorities] were guilty in this accident, we will not forgive" the loss of our loved ones, said a sombre Rouhani said, flanked by the heads of the judiciary and parliament as well as the chief of staff of supreme leader Ayatollah Ali Khamenei's office.

Rouhani called for a "fact-finding commission" into the disaster.

Saudi authorities have yet to provide a breakdown of the nationalities of the 769 Muslim pilgrims they say were killed, but many countries have announced the deaths of citizens.

Tallies of the dead from foreign officials and media from 24 countries put the toll at 1,036, well in excess of the Saudi figure.

With many more pilgrims still listed as missing, Iranian officials say the real toll is between 2,000 and 4,000.

The stampede occurred after two waves of pilgrims collided at the intersection of two streets.

One crowd had just finished a ritual in which pilgrims throw pebbles at three stone columns representing the devil - a rite central to Hajj - when it ran into another wave of people heading to perform the rite.

Sources close to the government said that some Hajj tours - which have an assigned time slot for allowing their groups to go to the Jamarat, where the rite is performed - had not abided by the schedule.